Only Connect: A Theorem about Learning and a Theorem about Primes

I will discuss two superficially unrelated results from recent work. The first is a speedup result in learning theory, stating that any fixed exponential-time learning algorithm for polynomial-size circuits can be speedup up to run in subexponential time. The second is a result about pseudo-deterministic generation of primes. I will try to give some intuition about the deep theory that allows us to prove disparate results of this kind.